Is it ever possible for the domain and range in a function to have different numbers of entries (for example, 3 domain entries to 5 range entries, or 2 range entries to 7 domain entries)? What happens when this is the case?

Question

anonymous · Answer

So it's possible for the range to have fewer entries than the domain but not vice versa.  If you think about it, if there were 3 entries in the domain and they mapped to 5 entries in the codomain, two of the entries would have to map to more than one entry, and it wouldn't be a function by definition of function.  That would just be a relationship.

If the domain consists of 7 elements and it maps to 2 elements in the codomain, then it is a function, but it's not one to one, because at least 5 of the elements in the domain map to something in the codomain that is already mapped to.

Two things to note: First, remember that every member of the domain has to participate in the function for it to be a function.  Secondly, the range is a subset of the codomain.  There can be a case where the codomain is 5 entries and the domain has 3, but the range cannot have more than 3 of the 5 entries in the codomain for that to be a function.